“The Last Days of Ptolemy Grey” (Riverhead Books, $25.95), by Walter Mosley

It’s been more than 20 years since Ptolemy Grey awoke to find his beloved but unfaithful wife, Sensie, lying dead in the bed next to him. On that day, his life began its downward spiral.

Now, at 91, he is frail and plagued by Alzheimer’s. The Los Angeles apartment he once shared with Sensie is filthy, filled with trash and overrun with vermin. He lives in terror of his drug-addicted neighbors, so he seldom ventures outside. Instead, he sits in front of the television for hours trying to remember how to turn it on. Some days, he forgets to eat.

His great-grandnephew Reggie looks in on him from time to time, taking him to the bank to cash his Social Security check and to the store for groceries. Then Reggie is killed in a drive-by shooting, and things get worse for Ptolemy. Reggie’s place is taken by another distant relative who comes by mainly to steal from the old man.

Mostly Ptolemy is left alone with what remains of his memories. “They were still his,” Walter Mosley writes in his new novel, but they were “locked on the other side of a closed door that he’d lost the key for. So his memory became like secrets held away from his own mind. But these secrets were noisy things; they babbled and muttered behind the door, and so if he listened closely he might catch a snatch of something he once knew well.”

The snatches are startling: a house fire consuming a childhood friend; the lynching of an old man Ptolemy had revered when he was a boy. The memories carry with them an overwhelming sense that Ptolemy has left something important unfinished, but he has no idea what it might be.

Mosley is best known for his critically acclaimed crime novels featuring Easy Rawlins, Socrates Fortlow and Leonid McGill; but he has always resisted being categorized, venturing into mainstream novels, science fiction and social commentary. Making an aged dementia patient the main character of “The Last Days of Ptolemy Grey” is the author’s most daring effort to date.

Ptolemy’s life changes when Robyn, a homeless 17-year-old girl Reggie’s mother had taken in, takes a liking to the old man and volunteers to take care of him.

First, she lugs in cleaning supplies, scrubs his filthy kitchen and bathroom, and, over Ptolemy’s initial objections, starts ridding the place of trash. The scenes in which Robyn and Ptolemy go through every item in his apartment, deciding which ones have meaning for him and which ones are just trash, are truly touching. So are the scenes in which Ptolemy gazes at the girl’s long legs and tries to suppress his impure thoughts — moments that would have come off as creepy in a lesser writer’s hands.

Once Robyn has cleaned Ptolemy’s space, she begins to work directly on him, taking him to a series of doctors who find that the old man is in remarkable physical condition for his age. Ptolemy could live with his worsening dementia for several more years, one doctor says, or he could choose to take an experimental drug that could restore his memories but dramatically shorten his life. Ptolemy looks into the doctor’s green eyes and senses that he is “staring into the face of the Devil.”

How Ptolemy responds to this Faustian bargain, and how he discovers and addresses the unfinished business that has long haunted him, provide the dramatic arc of this remarkable, beautifully written novel. “The Last Days of Ptolemy Grey” is a rich and profound exploration of generosity, greed, love, loss; the indignities of old age; the value of memory; and the true meaning of family.

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Bruce DeSilva is the author of “Rogue Island,” a crime novel published by Forge.